Cohomology of the toroidal compactification of A_3

TL;DR

This paper proves that the rational cohomology groups of the Voronoi compactification of the moduli space of abelian threefolds are isomorphic to its Chow groups, confirming a conjecture by Van der Geer.

Contribution

It establishes an isomorphism between cohomology and Chow groups for the specific case of the A_3 moduli space compactification.

Findings

Cohomology groups match Chow groups for the Voronoi compactification.

Supports Van der Geer's conjecture on the structure of these groups.

Advances understanding of the geometry of abelian threefold moduli spaces.

Abstract

We prove that the cohomology groups with rational coefficients of the Voronoi compactification of the moduli space of abelian threefolds coincide with the Chow groups of that space, as determined by Van der Geer.